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Computer-Aided Design for Microelectromechanical Systems (MEMS)

Y. C. Lee1, B. McCarthy2, Jiankuai Diao2 and Zhongxia Zhang3, and K. F. Harsh4 1 Professor, Department of Mechanical Engineering

2Graduate Research Assistant, Department of Mechanical Engineering 3Graduate Research Assistant, Department of Chemical Engineering

4Research Associate, Department of Mechanical Engineering

NSF Center for Advanced Manufacturing and Packaging of Microwave, Optical, and Digital Electronics (CAMPmode)

University of Colorado, Boulder, CO 80309-0427, USA leeyc@colorado.edu (e-mail address)

Abstracts With the advancements of MEMS foundry

services and CAD tools, MEMS devices can be cost-effectively designed and prototyped. Here, four designs that utilize these tools are presented: 1) a flexure design used to reduce the device warpage resulting from the mismatch in thermal expansion coefficients between the device and the substrate for flip-chip bonded MEMS, 2) a digitally positioned micro-mirror using multiple contacts, 3) a large MEMS flap that achieves uniform movement for fluid mixing, and 4) a three-dimensional, solder-assembled MEMS device that has been optimized for minimal deviation from the desired assembly angle.

Keywords: Microelectromechanical systems, computer-aided design, Coventor, optimization, optical MEMS, flexure

I. INTRODUCTION Microelectromechanical systems (MEMS)

technology enables the fabrication of both sensing and actuating devices that can be integrated with microelectronic, optoelectronic and microwave devices to create advanced microsystems. These devices, fabricated using semiconductor processing techniques, are very low cost while still achieving complex and precise nano-scale movements. Hundreds of MEMS-based sensors and actuators have been demonstrated, and the number of applications for them is growing [1]. Also, these micro-mechanical devices will be enabling components for many novel microsystems to be developed in the 21st century. The following quote from a US National Research Council’s 1997 report describes the potential impact of MEMS well. “Many people in the field of microelectromechanical systems (MEMS) share the belief that a revolution is under way. As MEMS begin to permeate more and more industrial procedures, not only engineering but society as a whole will be strongly affected. MEMS provide a new design technology that could rival, and perhaps even surpass, the societal impact of integrated circuits (ICs).” [2].

In general, there are four major activities critical to MEMS advancement. They are foundry fabrication, computer aided design (CAD), packaging and reliability.

During the last several years, progress in the establishment of foundry services and CAD tools has been very impressive. Figure 1 shows the cross-section of a well-known foundry process, MUMPs (Multi-User MEMS Processes), with its polysilicon and silicon oxide layers [3]. The oxide layers are sacrificial layers and are removed with HF after fabrication. MUMPS is only one example of the many surface micro-machining, bulk micro-machining, and LIGA foundry processes available today though.

Several foundry services, including MUMPs, also offer a cost-sharing program that significantly reduces low-volume prototyping costs. Rather than committing to a whole wafer, a research group can submit a design for a 1cmX1cm square. An example of such a design square is shown in Figure 2. That design is then integrated with others on the same wafer and the cost is split accordingly. Our research center takes this concept a step further. As can be seen in Figure 2, the 1cmX1cm square is divided up into 25 2mmX2mm sections that are allocated to individual researchers within the center. Thus, after the fabricated chips are received from MUMPs, they are sub-diced again to provide each researcher with his/her own design. In this way, an individual at an academic institution can fabricate a prototype for approximately $128 using the MUMPs process.

With foundry services well established, MEMS design, prototyping and manufacturing procedures are very similar to those established for application-specific integrated circuits (ASIC.) With this new manufacturing capacity, there is a need for a large number of educated MEMS designers who can design MEMS for integrated, application-specific microsystems. Fortunately, the newest versions of MEMS CAD tools are so user-friendly that any engineer can apply them to MEMS design after studying about 10 tutorials. As proof of this, we have developed a MEMS design course at the University of Colorado at Boulder. In only one semester, most of the students were able to learn and apply the CAD tool to the synthesis and analysis of original and useful MEMS designs.

Four such MEMS design cases are presented in

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the following sections. The first three designs are representatives of term projects carried out by the students taking the MEMS design course. The first case considers the flexure design that is the top concern in almost every MEMS device design. In particular, a flexure is optimized to reduce the effect of the thermal expansion coefficient mismatch between a silicon device and a ceramic substrate used for packaging. The second case illustrates the use of multiple contacts to achieve digital positioning for a novel micro-mirror. The third design focuses on the thermo-mechanical behavior through a design for MEMS flaps for enhanced fluid mixing. All the design work is carried out using Coventor’s CoventoreWare [4].

In addition, a fourth design case is presented with an automated design optimization procedure for a three-dimensional, solder-assembled MEMS device. Such an automated procedure is not available in the CAD tools today, but we would like to present this case since the procedure is so important that it should be part of most MEMS design activities. We expect MEMS CAD tools to include such a design optimization option in the near future.

II. FLEXURE DESIGN This first case details the optimization of a

flexure design that is used in many MEMS devices. Appropriate flexure designs are critical for MEMS because they are currently the only way to reliably allow for device movement and actuator control. Other options, such as rotating hinges and sliding contacts, are not yet reliable enough for the majority of MEMS applications [5]. However, due to processing limitations, it is often difficult to design flexures that are compliant enough in the desired direction while still providing enough resistance in other directions to prevent undesirable movement and stiction.

Figure 3 illustrates a typical case where a good flexure is needed [6]. Due to a difference in thermal expansion coefficients between the flip-chip bonded MEMS device and the substrate, cooling after bonding can cause the MEMS to buckle. As shown in Figure 3, flexures that could keep the device planar and intact would be extremely useful. To keep the device planar and intact, the flexure must be compliant in the in-plane axial direction while still being stiff enough in the out-of-plane z-direction to prevent stiction. The following optimization provides general trends in the flexure stiffness ratio that can be used in flexure design.

II.1 Method

Figure 4 shows the flexure design chosen for optimization. The optimization is done with AutoSpring, a CoventorWare module, by individually varying the fold length, fold spacing, and number of folds. These parameters are shown in Figure 4. AutoSpring provides an accurate representation of a typical flexure application because it moves the free end of a flexure through a range of specified displacements with a zero-slope

constraint at the free end of the flexure. The constraint is typical of MEMS flexures because they are normally attached to a larger moving plate (see Figure 3). For each displacement in AutoSpring, a reaction force and a spring constant are calculated. The spring constant values are then fitted to a second-degree polynomial so that nonlinear and linear springs can be analyzed.

For the optimization, each variation of the flexure design is submitted to AutoSpring where it is subjected to displacements of -10µm, -5µm, 5µm, and 10µm in both the vertical and axial directions. From the resulting spring constant polynomial, only the linear k1 value is used for comparison because the k0 coefficient is zero without the presence of residual stress and the k2 coefficient is generally several orders of magnitude less than k1, indicating that the nonlinear effect is fairly small. This agrees with the expectation that the flexures behave elastically and linearly.

The goal of the optimization is to maximize z-stiffness or bending stiffness while minimizing x or axial stiffness. The stiffness ratio of z-stiffness to x-stiffness is calculated and plotted for each case to better observe trends in the flexure behavior. In this case a higher stiffness ratio is desirable because maximum x-displacement for a given z-displacement means the flexure can absorb a significant mismatch in thermal expansion coefficients without succumbing to stiction.

II.2 Results

Before proceeding with the optimization, a partial validation of the model is done by comparing the CoventorWare and analytical results for a basic cantilever beam. This validation confirms that the 2 x 2 x 1.5µm 27-node, brick element size is acceptable for predicting displacements. Following the model validation, a total of 36 separate analyses are carried out for the optimization. A total of four fold lengths, 10, 30, 50, and 70µm are used. For each fold length, three fold spacings are used, and for each fold length and fold spacing combination, three configurations using one fold, two folds, and three folds respectively are analyzed. These parameters are displayed in Figure 4 for reference. Finally the distance from the fixed end to the free end of all flexures is kept to 50µm for the sake of comparison and because many flexures are designed to fit in a pre-defined space. The only exception is the case with three folds and a 10µm fold spacing, which takes up more room by definition. Surface plots of the z-stiffness to x-stiffness ratio for all cases are shown in Figure 5, where a cubic interpolation formula is used to plot the surface between data points.

The plots in Figure 5 indicate that fold length is the most critical parameter in determining the stiffness ratio. For example, increasing the fold length from 10µm to 70µm for the 1 fold case with a 5 µm fold spacing provides a 2000% increase in the stiffness ratio. The dominance of the fold length parameter is partly because the values used cover a much wider range than the other

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parameters, but that also reflects typical MEMS design constrains. It is normally easier to vary the fold length to a greater extent than it is to vary the number of folds or fold spacing given an axial length constraint. The fold spacing is also an important factor as smaller spacing provides significantly better performance. For instance going from 10µm spacing to 5µm spacing for 2 folds and a 70µm fold length yields a 21% increase in the stiffness ratio. The one parameter that does not have a large effect is the number of folds. Going from 1 fold to 3 folds with a 70µm fold length and 5µm fold spacing yields a 4% decrease in the stiffness ratio. In this case, there is only a small change because the two stiffnesses are decreasing at the same rate as the number of folds increases. In summary, an optimal flexure design will include the longest fold length and smallest fold spacing possible. The number of folds can then be used to tailor the stiffness to a given application.

III. DIGITALLY POSITIONED MICROMIRRORS

This next case moves from the individual component level to the device level as it details the improvement of a digital micromirror design through simulation. Digital micromirrors will be key devices for many optical applications where precision position control is required such as optoelectronic modules for optical communication, free space optical interconnects, optical switching and other systems [7-9]. In these applications, digital devices are preferred over analog ones because the analog devices require complicated closed-loop control electronics, which result in high cost and power consumption. A micro-mirror with precise, digitally controlled positioning or tilting does not suffer from the analog limitations, however. Thereby, it can use open-loop control electronics, reducing the system complexity and power consumption.

III.1 Method A novel multilevel digital micromirror design has been reported by Zhang et al. [10]. The primary design of the digital micromirror and its principle of operation are shown in Figure 6, where 6-(a) shows a SEM picture of the mirror, which is fabricated using MUMPs. The mirror is connected to its supporting beams by two flexures. The two electrostatically driven legs along the other two sides of the mirror are designed to tilt it in the positive and negative directions. The poly2 layer is used for each leg or top electrode, which is made of four identical plates connected by thin, flexible beams. The bottom electrodes, constructed of poly0, are four separate plates located right under the top electrode, each of which can be supplied with voltage independently and sequentially to define the tilting angles of the mirror. As illustrated in Figure 6-(b), the snap-down of each successive electrode section corresponds to a separate digital angle. Also, to achieve a larger rotation range pre-stressed beams are used for the support beams to increase the gap between the top and bottom electrodes [11].

Although the digitally positioned micromirror has been fabricated and has shown good performance in preliminary experiments, the desired precise digital control has not been completely obtained. The mechanical structure needs to be modified and optimized To optimize the mechanical structure, the CoventerWare finite element code with 27-node brick elements is used. Through a careful study of the effects of mesh size on the convergence time and accuracy, the most efficient finite element meshes for the top beam contain extrude solid elements with the largest dimension specified as 50 µm. Manhattan elements with a size of 10µm x 10 µm x 5 µm are used for the bottom electrodes. As shown in Figures 7-a and -b, due to symmetry, only half the device is modeled. Simulations predict the combined mechanical and electrostatic behavior of the micromirror; bimorph support beams and movable drive legs as a total system. Some minor structures such as dimples, etch holes, etc. are removed for simplification. First, the bimorph effects used to generate the large initial gap are simulated and compared to the deformation observed in experiments. The model’s z-displacement is 14.0 µm, which is close to the experimental result of about 13.2 µm. In addition, due to warpage, there is an initial angle of about 0.7° measured; this angle is simulated by applying a uniform downward load (0.0005Mpa) on the top beam. Finally, in the MUMPs process, the height of the dimples used between the top electrodes and the substrate is 0.75 µm. This distance is used as a surface constraint for the top electrode in the model to terminate vertical surface movement before contact between the electrodes occurs. CoventorWare’s Cosolve module is used to simulate the hysteresis behavior of the model. In order to precisely simulate the digitally controlled tilting behavior of the mirror, a two-volt increment is used.

III. 2 Results Using the simulation results, the tilting angles

of the mirror are calculated and plotted as a function of the applied voltages. These model results are shown in Figure 8 where they are compared to experimental results as well. During the experiment, the mirror’s tilting angle jumps from 0.36 to 2.8 degrees when the voltage reaches 19.4 Volts. The angle then increases to another level at 3.5 degree with 22 Volts applied. At this voltage all the electrodes collapse onto the substrate and there are no further angle changes even if higher voltages are applied. When the voltage is reduced, the angle remains constant because the release voltage corresponding to the two closely connected surfaces is usually much lower than the pull-down voltage. At 6.2 Volts, the angle is shifted from 3.5 to 1.9 degrees. At 4 Volts, the angle is changed again from 1.9 to 0.9 degrees. As mentioned before, these digital angles with levels of 0, 2.8, 3.5, 1.9 and 0.9 degrees can be used to simplify control electronics for optical switches. Of course, the flatter and the longer these stages, the better for the digital control. The MEMS device’s performance measured demonstrate the feasibility of the digital positioning concept, but it needs to be optimized for

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better digital performance.

As shown in the figure, the agreement between the experiment and the simulation with 0.75 µm dimple is not very good. The voltages required for the pull down process are too high, and the number of digital levels is different from the measured one. During the experiment, the first two electrodes collapse at the same time and result in a single digital angle of 2.8 degrees. With 0.75 µm, however, these two electrodes collapse sequentially and result in two different digital angles. It is clear that the 0.75 µm assumed needs to be modified for this particular device measured.

If the top electrode-to-solid surface gap is changed to 0.1 µm, results are close to the measured angle-vs-voltage relationship. The magnitudes are close and the numbers of digital levels are matched. But, it should be noted that the simulated results are not mesh independent. Finer meshes cannot be used due to the limitations of the computer hardware. As a result, 0.1 µm should be used as a reference only. It is difficult to determine the correct gap resulting from the use of dimples. More studies are needed to characterize this gap. Nevertheless, the simulations provide us with a more insight into the digital positioning. Large gap is desirable for the future device design because it achieves a higher number of digital angles and the voltage region for each digital angle is flatter than those cases with only 0.1 µm gap.

After a series of trial-and-error simulations with different flexures, support beams and plates, a better performing design is developed and is shown in Figure 9. The dimensions of the three electrostatically driven plates are increased sequentially from the center region to the end away from the mirror. The positions of the three top plates are also moved towards the mirror for better tilting. This design is the “Modified Design –1.” It is further improved to be “Modified Design –2” by increasing the width of the flexures to adjust tilting angles. The simulation results for the three designs are shown in Figure 10. Because 0.75 µm is the goal for the future device designs, this is the gap used for the study. Compared with the original design, the Modified Design –1 is an improvement because it adds a new, third digital level. The Modified Design –2, with the wider flexures, adjusts the tilting angles further so they approach a more uniform distribution with angles close to 1, 2, 3 and 4 degrees, respectively.

The comparisons among different designs and gaps demonstrate that an already working device can be improved through the use of simulation without the need for prototyping. The model of the initial micromirror design provides the nature of the relationship between the numerical and experimental results. The subsequent revisions to the model show that device performance can be improved by modifying the shape and placement of

individual electrodes as well as widening the flexures.

IV. MEMS FLAPS FOR FLUIDS MIXING The third case turns from the demonstration

of a MEMS device for a generic application to the modification of a generic MEMS device for a specific application. In this case, MEMS microactuators for the purpose of enhancing fluid mixing are improved through the use of simulation [12]. In the field of fluid mechanics, precise control over a given flow is often necessary. Here, MEMS are used as the controlling mechanism. The flow geometry to be controlled is presented in Figure 11. The actuators are mounted on either side of the jet, providing a disturbance that is naturally amplified as it travels downstream. The driving mechanism for the first set of flaps is electro-thermal, which is capable of providing both the deflection and force necessary to disturb the flow [12]. The actuators are mounted on a ceramic substrate using flip-chip bonding with solder. This approach allows for several MEMS actuators to be accurately positioned on a ceramic substrate, which is then placed next to the jet. The effect of the actuators is significant, as shown by the images in Figure 11. In the absence of forcing, flow is laminar and featureless; however, when excited, large-scale vortices arise that enhance the mixing of the jet with the surrounding air. This phenomenon is known to have a profound effect on combustion processes.

IV.1 Method Although the electro-thermal flaps have been

shown to work, a new design driven by electrostatic forces is being developed to simplify the fabrication procedure. A model of the new design is shown in Figure 12. The flap is composed of poly2 and gold strips. The gold-on-polysilicon bimorph effect lifts up the plate, and the applied electrostatic voltage moves the plate back toward the substrate to create the air puffs for fluid mixing. This design is a scaled up version of the bimorph design reported in [11]. The size of the flap is about 300µm × 900 µm.

For the first part of the simulation, the creation of the initial gap by the bimorph effect is modeled, wherethe stress-free temperature is assumed to be 75 oC. Figure 13 shows the displacement of the flap when the temperature drops from 75 to 20 oC . Because of the symmetry of the device, only half of the flap is simulated. The maximum displacement of about 25um in the z-direction occurs at the edge of flap. This is an increase from the initial 2.75 µm gap between the nitride and poly2 layers to what is now a 27.75 um gap. The large displacement achieved with such a large gap is needed for the flap to purturb the fluid. However, there are two major problems in this design:

• The z-displacement along the y-direction (Figure 13) is not uniform and the maximum z-displacement occures at the end of the device. This is not desirable for 2-D flow control. The

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z-displacement should be more uniform in the y-direction.

• The pull-down voltage calculated is about 103 V, which is too high for this particular application.

These two problems are solved by subsequent design improvements. The first improvement is the optimization of the gold strip widths on each flap to achieve a uniform displacement. Figure 13 shows that the gap is larger at the end than that at the middle. As a result, to get a uniform gap the gold strips are made narrower at the end. Assume the gap d is a functional of the strip width:

)1())(( ywfd = The design objective is to find a width

distribution w(y) such that d becomes a constant. Assume w(y) is continuous and differentiable up to as many terms as needed. We can expand the w(y) as Taiylor’s series:

)2()()( 2210 L+++=

lyc

lyccyw

where l is the length from the center of the gold

strip in the middle to the center of the gold strip at the end. The origin of y is at the center of the middle gold strip. The direction of y is opposite to the y-direction shown in Figure 13 though. For simplicity, using the first-order guess of w(y), we can get

)3()1()(0

1010 l

yccc

lyccyw +=+=

In simulation 0c is set to be the width of the

middle gold strip, so there is only one variable, 1c , to be determined. The y can only take discrete values such that:

)4(nm

ly

=

where n is the total number of gold strips in the half flap and m means mth gold strip from the center and takes values: 1,,2,1,0 −= nm L . The width of the gold strips varies according to this linear distribution. An appropriate c1 is calculated for a uniform gap along the y-direction. The bifurcation method used is described as follows:

• Assuming 10

1 −=cc

, the vertical

displacement is larger at middle.

• Assuming 00

1 =cc

, the vertical

displacement is larger at end. There

exists a value of )0,1(0

1 −∈cc

such

that the displacements at end and at middle can be the same.

Continuing the iteration several times, the value of 0.8 for the ration is found to meet the uniformity requirement.

IV.2 Results Figure 14 shows the width distribution of the gold strips and the z-displacements at the edge. The difference in z displacement at edge along the y direction is reduced from about 4µm (Figure 13) to about 1µm (Figure 14). In addition, the design is further improved to reduce the pull-down voltage by using flexures to connect the flap plate to the anchor. Figure 15 shows the improved model and the corresponding simulaton results.

Here 6.00

1 −=cc

is used, which is obtained by the

bifurcation method introduced above. Such flexures reduce the pull-down voltage from 103 to 70 Volts. In this case, the stress-free temperature is assumed to be 170 oC due to a thermal annealing following fabrication. In summary, electrostatic microactuators to control a planar jet have been designed using simulation. Design iterations in Coventorware resulted in a more uniform actuator tip displacement and a reduction in actuation voltage from 103V to 70V.

V. OPTIMIZING MEMS FOR SOLDER

SELF-ASSEMBLY The final case does not involve the use of CoventorWare for design iteration or optimization, but rather introduces a more advanced type of automated optimization. As MEMS devices progress and become more elaborate, understanding the complex interactions between the many possible design variables becomes difficult to accomplish by manually running all the design iterations in a MEMS CAD software package available today. One solution to this type of problem is the use of automated design optimization algorithms to find appropriate design variations. This methodology is common in engineering design but is vastly underutilized for MEMS.

The design to be presented is for solder-assembled, 3-D MEMS devices [13]. One of the most common methods for manufacturing MEMS devices is by using surface micro-machining. Due to the nature of thin film deposition technology, a fundamental problem with surface micro-machining is its inability to produce highly three-dimensional structures. A common solution is to fabricate flat, 2D hinged components that can be lifted or rotated into assembled structures. Such structures are very common in many MEMS and microelectronics fields, namely micro-optics [14]. The draw back of hinged designs is that they need to be assembled after fabrication. The traditional way to perform this assembly is to do it manually or use additional MEMS mechanisms to assemble devices automatically [15,16]. Manual assembly usually consists of rotating the plates by hand using high precision micro-manipulators. This form of assembly is not practical for mass assembly and manufacturing though, and is rarely effective. Mechanism driven assembly is also insufficient because these MEMS mechanisms are often large and complex, and thus negate many advantages inherent in MEMS devices.

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A new method of assembling MEMS has been developed that has made cost-effective mass manufacturing of assembled 3D MEMS structures both practical and feasible. This method uses the surface tension properties of molten solder or glass as the assembly mechanism [17-19]. The solder method involves using a standard hinged plate with a specific area metalized as solder wettable pads. Once the solder is in place, it is heated to its melting point, and the force produced by the natural tendency of liquids to minimize their surface energy pulls the free plate away from the silicon substrate (Figure 17). Solder is a predominant technology for electronics assembly and packaging. It is not only used for electrical connections, but also for sub-micron accuracy alignment in many packaging applications such as optoelectronic passive alignment [20]. Using solder, hundreds or thousands of precision alignments can be accomplished with a single batch reflow process, and the cost/alignment can be reduced by orders of magnitude. In addition, solder provides high quality mechanical, thermal and electrical connections.

Figure 18 is an actual solder self-assembled plate that is 400 microns square and was assembled with an approximately 200 micron diameter solder sphere. With the development of this technology, the focus of work on solder self-assembly has changed from demonstrating that hinged MEMS can be assembled, to refining the precision to which they can be assembled. The predominant source of error is the deformation that results from process-induced stresses within the structure. The deformation is reduced by using finite element modeling and optimization algorithms to optimize the solder self-assembly structure for maximum assembly angle precision.

V.1 Method The basic building block of a solder self-

assembly structure consists of a single solder sphere with a hinge and mechanical lock on either side (Figure 19). A typical plate is between 100-500 microns on either side. A 600 micron wide by 200 micron tall structure is chosen for optimization because ample experimental samples are available to confirm the predictions. For this case, the parameters to be varied are: the contact position of the mechanical lock and plate, the width and height of the solder pad, and the position of the hinge. The only constraint is that the solder pad should remain large enough to be practical for solder deposition processing. The finite element software ABAQUS is used to model the structure and extract relevant data, and the optimization algorithm NLPQL [21] is used to optimize the variables. The optimization process is as follows: starting with an initial guess for the variables, the model results and the derivative of those results with respect to each variable is evaluated. These guesses are used to create an ABAQUS input file, which is then processed, and the results extracted. Since this is not an analytical function to be optimized, the derivatives are found using a simple finite difference method. These values are then used by the NLPQL program to generate

a new prediction. This process is repeated until the solution converges to some desired tolerance. Since this process could run for many iterations, it is important that an efficient model is used. For this reason Kirchoff composite shell elements are used over standard 20 node 3D solid elements. The resulting computation time per model evaluation is reduced by approximately 95%. The average time to converge to an optimum solution, when run on a 500 MHz DEC Alpha (DEC personal workstation model 500au) with 768 MB of RAM running DEC Unix V4.0 is about 30 minutes and involves ten step iterations and 40 model evaluations.

The plate is modeled using composite shell elements, but the solder is simulated with standard three-dimensional solid elements. The interaction of the kickstand and hinges is modeled using contact surface approximations rather than by including the actual hinge and kickstand structure into the model. This greatly increases the computational efficiency of the model without affecting accuracy. The accuracy of the model is gauged by comparing the predictions to experimental data. Figure 19 shows one such comparison in which a 200 by 1800 µm solder self-assembly plate is modeled, fabricated, and measured interferrometrically. It is found for all cases that the model prediction fell within the data variation.

After validation, the optimization program is able to generate a prediction that significantly optimizes the deformation in the plate. The values to be minimized are the rms, average, and maximum deflections of the plate. Figure 20 shows three sample cases for one design optimization problem: a) a prediction in which there is no lock or hinge contact, b) a prediction in which the lock contact position and hinge have been placed, and c) the algorithm prediction for lock, hinge position, and pad dimensions that will result in minimum deformation. Interestingly, the case in which the lock and hinge are placed poorly resulted in a more severe deformation than with no lock at all. The poor lock and hinge position results in a maximum deflection of ~5.5 µm and a rms deflection of ~3.4 µm, whereas, the prediction with no lock or hinge results in a max deflection of ~4 µm and an rms deflection of ~2.1 µm. Finally, the optimized structure shows a significant improvement with a maximum deflection of ~0.9 µm and rms deflection of ~0.6 µm.

The reason for the reduced deformation is likely due to the lock and hinge constraints working against the deformation resulting from solder shrinkage. The shrinkage tends to cup the plate around it like a shroud. By placing the hinge and lock near the edge of the plates, they restrict the plate and force it back toward the desired position. If the lock and hinge are placed too close to the solder, they only amplify the deformation. If there are too far out, the plate will bend significantly between them and the solder joint.

The above work discusses the reduction of plate deformation through design optimization. However, the primary point of this optimization is angle precision. The

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question is, with plate deformation, how precise an angle can still be achieved ?

In one experiment, a design for a 400µm-by-400µm-by-3.5µm basic solder assembly structure is optimally design and fabricated. Six of these structures are then assembled and measured. The average angle of assembly is 89.78o. More importantly, the maximum deviating sample was at 89.69o, which is a mere 0.09o angle deviation from device to device. This demonstrates assembly repeatability, and repeatability is really what is important. The devices are designed to rotate to 90o , and are off by approximately 0.2o. By changing a design parameter (the length of the lock) this number can be reduced and the variation in angle precision will be the maximum angle deviation from device to device (in this case 0.09o). Thus, the discussed automated optimization procedure can in fact determine the relationship between a variety of variables and use that relationship to optimize a specific structure.

VI. CONCLUSIONS Using the MUMPs foundry service and the

CoventorWare MEMS CAD tool, students at the University of Colorado – Boulder have been able to carry out numerous original and useful MEMS designs. Three representative designs have been reviewed: 1) a flexure design used to reduce the device warpage resulting from the mismatch in thermal expansion coefficients between the device and the substrate for flip-chip bonded MEMS, 2) a digitally positioned micro-mirror using multiple contacts, and 3) a large MEMS flap that achieves uniform movement for fluid mixing. In addition, an automated design optimization procedure has been developed for a three-dimensional, solder-assembled MEMS device. Its optimization procedure for the minimal deviation from the desired assembly angle was presented and discussed.

VII. ACKNOWLEDGMENTS

The authors would like to express their appreciation to Coventor, Inc. for their software support for the establishment of the MEMS design course at the University of Colorado – Boulder. CoventorWare has been used as the MEMS CAD tool for the first three design cases presented. The fourth design case was supported by the Defense Advanced Research Projects Agency (DARPA), the Air Force Research Laboratory, Air Force Materiel Command, USAF, under agreement number F30602-98-1-0219. In addition, we would like to thank Mr. Jianglong Zhang and Mr. Zhichun Ma for their collaborations during the designs of the digitally positioned MEMS and the MEMS flaps.

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Su, and M.-C Wu, “MEMS technology for optical crosslinks for micro/nano satellites,” in Proc. Int. Conf. On Integrated Nano/Microtechnology for Space Applications, Houston, TX, Nov. 1-6, 1998.

10. Jianglong Zhang, Y.C. Lee, Victor M. Bright,

John Neff, "Digitally Positioned Micromirror For Open-Loop Controlled Applications," The Fithteenth IEEE International Conference on Micro Electro Mechanical Systems (MEMS 2002), Las Vegas, Nevada, USA, January 20-24, 2002.

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11. D.C. Miller, W.G. Zhang and V.M. Bright,

“Micromachined, flip-chip assembled, actuatable contacts for use in high density interconnection in electronics packaging,” Sensors and Actuators A: Physical 89 (1-2) (2001) pp. 76-87.

12. Zhichun Ma, T. Peacock, E. Bradley and Y.C.

Lee, “Solder-Assembled MEMS Flaps to Enhance Fluid Mixing,” Proceedings of 2001 ASME International Mechanical Engineering Congress and Exposition, November 11-16, 2001, New York, NY.

13. Kevin F. Harsh, Victor M. Bright, Yung-Cheng Lee, "Design Optimization of Surface Micro-machined Self-assembled MEMS Structures,” The ASME International, Intersociety Electronic & Photonic Packaging Conference & Exhibition (InterPACK'01), Kauai, Hawaii, July 8-13, 2001.

14. N.C. Tien, M. Kiang, M.J. Daneman, O.

Solgaard, K. Y. Lau, and R.S. Muller, “Actuation of Polysilicon Surface-Micro-machined Mirrors”, SPIE Proceedings, Vol. 2687, 27 January-2 February, 1996, San Jose, CA.

15. T. Akiyama, D. Collard, H. Fujita, “Scratch

Drive Actuator with Mechanical Links for Self-Assembly of Three Dimensional MEMS”, Journal of Micro-electromechanical Systems, Vol. 6, No. 1, pp.10-17, 1997.

16. L. Fan, M.C. Wu, K.D. Choquette, “Self

Assembled Micro-actuated XYZ Stages for Optical Scanning and Alignment”, Transducers 97: 1997 International Conference on Solid-State Sensors and Actuators, Chicago, June 16-19, 1997.

17. K. F. Harsh, V. M. Bright, and Y. C. Lee,

“Solder Self-Assembly for Three-Dimensional Micro-electromechanical Systems,” Sensors and Actuators A, vol. 77, pp. 237-244, 1999.

18. P.W. Green, R.R.A. Syms, E.M. Yeatman,

“Demonstration of Three-dimensional Microstructure Self-Assembly”, Journal of Micro-electromechanical Systems, vol. 4, no. 4, pp.170-176, 1995.

19. R.R.A. Syms, “Rotational Self-assembly of

Complex Microstructures by Surface Tension of Glass”, Sensors and Actuators A, v65, pp. 238-243, 1998.

20. Q. Tan, Y.C. Lee, “Soldering for Optoelectronics Packaging.” IEEE Electronic Components and Technology Conference, Orlando, FL, May 28 - 30, 1996, pp.26-26.

21. K. Schittkowski, “NLPQL: A Fortran subroutine for solving constrained nonlinear programming problems”, Annals of Operations Research, Vol. 5, 485-500 (1985/86)

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0.6

2.0

0.75

2.0

1.50.5

Layers and Nominal Thickness in Microns

0.5

MCNC0.6

2.0

0.75

2.0

1.50.5

Layers and Nominal Thickness in Microns

0.5

MCNC Figure 1: Cross-sections of MUMPS (Multi-User MEMS Processes) Foundry Process

Figure 2: A typical 1cm X 1cm chip design using MUMPS

10

400 µm

40 µm

110 to 25 oC

Flexure 400 µm

40 µm

110 to 25 oC

Flexure 400 µm

40 µm

110 to 25 oC

Flexure 400 µm

40 µm

110 to 25 oC

Flexure

Figure 3: Warpage of a MEMS variable capacitor resulting from thermal mismatch between silicon MEMS device and alumina substrate. Flexures can be used to reduce the warpage.

Fold Length

Fold Spacing

Number of Folds

Fold Length

Fold Spacing

Number of Folds

Figure 4: Parameters for the flexure design

Figure 5: Optimization plots for flexures with different stiffness ratios

11

Top electrod

Bottom electrode

Pre-stressed beam

Mirror surface

Top electrode Micromirror

Bottomelectrode

(a) Original position of micromirror

(b) One electrode “snap down”

(c) Two electrodes “snap down”

(d) Three electrodes “snap down”

(e) Four electrodes “snap down”

Top electrode Micromirror

Bottomelectrode

Top electrode Micromirror

Bottomelectrode

(a) Original position of micromirror

(b) One electrode “snap down”

(c) Two electrodes “snap down”

(d) Three electrodes “snap down”

(e) Four electrodes “snap down” Figure 6: (a) SEM photo and (b) pperating principle of the digitally positioned micromirror

(a) (b) Figure 7: a) model for the simulation of the digitally positoned mirror and b) an example of the tilting angles simulated

12

0

1

2

3

4

5

6

0 20 40 60 80 100

Voltage Applied (v)

Tilti

ng A

ngle

s of

the

Mirr

or (d

egre

es)

Experimental Results

Simulation with 0.1 micron

Simulation with 0.75 micron

Figure 8: Simulation results of the digital micromirror

Original design Modified designOriginal design Modified design

Figure 9: Original and modified designs

13

Figure 10 Simulation results of the modified designs

Instabilitiesare

born here

MEMS

Figure 11: The arrangement of MEMS flaps used to enhance fluid mixing. Flaps are placed on either side.

Figure 12: Solid model with gold, polysilicon and nitride layers

0

1

2

3

4

5

0 20 40 60 80 100Voltage Applied (v)

Tilti

ng A

ngle

s of

the

Mirr

or (d

egre

es)

Original DesignImproved Design -1Improved Design -2

14

Edge

End

Middle

y

Edge

End

Middle

y

Figure13: Contour of vertical z-displacement and the z-displacements at the edge of the flap along the y-direction.

Figure 14: Optimized flap design and its z-displacements at the edge of the flap along the y-direction

Figure 15: Optimized flap design with flexures and its z-displacements at the edge of the flap along the y-direction

15

(1)

Hinged Plate

Substrate

(2)HingedPlate

Substrate Figure 16: Illustration of solder self-assembly of hinged MEMS plate. (1) During reflow. (2) Equilibrium position.

Figure 17: Solder assembled three-dimensional MEMS device with kickstands

1800 µm

200 µm

Interferrometricmeasurement of out ofplane deformation

Figure 18: Validation example in which the model prediction (bottom) matches the interferometric measurement (top right)

16

Figure 19: Comparison of results: (top) prediction when no lock or hinges are used, (middle) prediction when lock and hinge position are poorly chosen. (bottom) prediction for optimum pad size and lock/hinge position.